1. Warm Up 8.2, Day 1
Translate into an equation.
r varies inversely with t.
c varies directly with s and inversely with h.
t varies jointly with r and s and inversely with the cube of h.
Describe how to tell if a set of data shows direct or inverse variation.
y varies inversely with x. When y = 10, x = Find y when x = 30.

2. Graph simple rational functions (8.2)
Unit 8: Rational Functions
Target 8.2, Day 1
Graph simple rational functions (8.2)

3. Graph
Hyperbola
Domain:
Range:
Vertical Asymptote:
Horizontal Asymptote:

4. Graph and compare to
Domain:
Range:
Vertical Asymptote:
Horizontal Asymptote:
What do you think would happen if the 6 was -6?

5. h is ___________________ shift (this will tell you the domain and where the vertical asymptote is, x = h)
k is ___________________ shift (this will tell you the range and where the horizontal asymptote is, y = k)
If a is positive, the branches of the hyperbola will lay in the 1st and 3rd Quadrants. If a is negative the branches will lay in the 2nd and 4th Quadrant. The bigger a is, the farther the branches will be from the axes.

6. Graph . Start by drawing the asymptotes. Then
state the domain the range.
Domain:
Range:
Vertical Asymptote:
Horizontal Asymptote:

7. Start by finding the zero(s) of the denominator
Start by finding the zero(s) of the denominator. This is the vertical asymptote (and domain).
Graph
To find the horizontal asymptote (and range), divide the leading coefficients.
D: ________ VA: ________
R: ________ HA: ________

8. Start by finding the zero(s) of the denominator
Start by finding the zero(s) of the denominator. This is the vertical asymptote (and domain).
Graph
To find the horizontal asymptote (and range), divide the leading coefficients.
D: ________ VA: ________
R: ________ HA: ________

9. Warm Up 8.2, Day 2
State the domain, range, vertical asymptote, and horizontal asymptote for each function.
D: ________ VA: ________
R: ________ HA: ________
D: ________ VA: ________
R: ________ HA: ________
D: ________ VA: ________
R: ________ HA: ________
D: ________ VA: ________
R: ________ HA: ________

10. Graph general rational functions (8.3)
Unit 8: Rational Functions
Target 8.2, Day 2
Graph general rational functions (8.3)

11. When graphing rational functions, keep the following in mind:
Zeros of numerator = x-intercepts
Zeros of denominator = vertical asymptotes
The horizontal asymptote (if there is one) depends on the degree (highest exponent) of the numerator and denominator
Top < Bottom
Top = Bottom
Top > Bottom
No Horizontal Asymptote
But....

12. Identify the x-intercepts, vertical asymptotes, and horizontal asymptotes of the graph. Then sketch the graph.
x-Intercepts: ____________
Vertical Asymptotes:___________
Horizontal Asymptotes:________

13. x-Intercepts: ____________
Identify the x-intercepts, vertical asymptotes, and horizontal asymptotes of the graph. Then sketch the graph.
x-Intercepts: ____________
Vertical Asymptotes:___________
Horizontal Asymptotes:________

14. x-Intercepts: ____________
Identify the x-intercepts, vertical asymptotes, and horizontal asymptotes of the graph. Then sketch the graph.
x-Intercepts: ____________
Vertical Asymptotes:___________
Horizontal Asymptotes:________